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Available online at www.sciencedirect.com

Nuclear Engineering and Design 238 (2008) 577–589

CFD simulation of the Vattenfall 1/5th-scale PWRmodel for boron dilution studies

T.V. Dury a,∗, B. Hemstrom b, S.V. Shepel c

a Paul Scherrer Institute, Thermal-Hydraulics Laboratory, 5232 Villigen PSI, Switzerlandb Vattenfall Utveckling AB, Alvkarleby, Sweden

c Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

Received 26 September 2006; received in revised form 30 January 2007; accepted 23 February 2007

bstract

The VATT-02 experiment, performed at Vattenfall, Sweden, with a 1/5th-scale model of a 3-loop PWR pressure vessel, has been simulatedith the computational fluid dynamics (CFD) code CFX-5 at PSI, Switzerland. The simulations were initially part of the FLOMIX-R EU 5th

ramework Programme, aimed at providing validation data prior to CFD codes being used to model full-size nuclear vessels. These studies werextended at PSI to examine mesh effects. Steady-state velocities and transient boron concentration distributions were plotted, and their sensitivityo different CFD models and mesh refinement examined. Steady-state velocities in the downcomer were not in good agreement with experiment atll instrumentation locations, but, nevertheless, predicted transient boron distribution and its minimum concentration at the core inlet were closeo the measured data. Useful conclusions could be drawn for application to full reactor size.

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2007 Elsevier B.V. All rights reserved.

. Introduction

There exists a potential risk of a reactivity accident occurringn a pressurised water reactor (PWR) if a slug of water with a lowoncentration of boron (as reactivity inhibitor) passes into theessel and core under certain conditions of reactor cooling pumpRCP) start-up. This could happen by accident if the reactor ist decay heat level and natural circulation has been stopped. It isherefore essential to determine if a substantial reactivity changeould occur. This would be carried out by using neutronics codesfter the distribution of the degree of boration of the fluid withinhe core is known.

The present CFD study began as a contribution to theLOMIX–R Project of the 5th EURATOM Framework Pro-ramme (Rohde et al., 2005a) initiated as a follow-up to theth Framework EUBORA Concerted Action (Tuomisto, 1999).

he computational fluid dynamics (CFD) codes FLUENT–6

FLUENT Inc., 2005) and CFX-5 (ANSYS Inc., 2006) weresed to simulate the VATT–02 experiment performed in the test

∗ Corresponding author. Tel.: +41 56 3102734; fax: +41 56 3104481.E-mail address: Trevor.dury@psi.ch (T.V. Dury).

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029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2007.02.038

acility at Vattenfall Utveckling AB, Alvkarleby, Sweden—a/5th-scale model of the pressure vessel and internal compo-ents of a 3-loop Westinghouse PWR, with pump flow-rateehaviour applied corresponding to RCP start-up under vari-us non-design operating conditions. This report refers onlyo the results obtained with CFX-5, as these were closer tohe measured data for both steady-state and (particularly) forransients.

The object of the CFD study was to: (a) simulate steady-stateonditions with constant flow in one cold leg and the pumps inhe other two legs stopped; (b) compare predicted and measuredelocity distributions within the downcomer at given verticallanes; and (c) simulate a transient experiment in which thequivalent of a plug of water with a lower boron concentrationas injected through this single cold leg at a known rate andith a known total volume.

. Experiment

CFD calculations were performed by PSI for the VATT–02est from the Vattenfall series of four experiments, VATT–01 toATT–04. All tests were slug mixing transients, representing alug of low boron concentration initially present in one of the

578 T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589

rsosgn

P

Fig. 1. Vattenfall 1/5th-scale PWR model facility.

eactor coolant system (RCS) pipes. A photograph of the centralection of the model facility is shown in Fig. 1, with a schematicf the full facility layout given in Fig. 2 and a vertical cross-ection of the model reactor vessel in Fig. 3. All dimensions

iven in Fig. 3 are in millimetres, and are for the model facility,ot for the plant.

All external model components were constructed oflexiglas®, to allow flow measurement and visualisation to be

Fig. 2. Schematic representation of the facility.

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Fig. 3. Vertical cross-section of the vessel.

ade. As the core was not modelled, or flow within it exam-ned, the core outlet was modified in the facility to allow fluido exit vertically instead of via the hot-leg penetrations in theessel wall. Internal model components were either constructedf Plexiglas® or steel, and instrumentation in the lower vessellenum was incorporated within support columns connecting theifferent horizontal support plates in the region from the base ofhe dome up to the core inlet plate.

The model used tap water to simulate the borated water orig-nally within the system, heated to 53.6 ◦C to maximise theeynolds number (Rohde et al., 2005b). The supply tank for the

ap water had a volume of 15 m3, in the form of a horizontal cylin-er with a length of 6 m and diameter of 1.8 m. The water levelithin it was kept at approximately 200 mm below the roof of

he tank and was relatively stable during transient experiments.eat-loss effects on slug volume and mixing are recognised, butave been impossible to quantify. They are, however, thought toe relatively small.

Water with relatively low boron content (for the slug) wasepresented by a salt–water solution, with a suitable amount ofn organic fluid added, with a lower density than water, to bringhe average mixture density so close to that of the tap waterhat buoyancy forces were negligible. This slug fluid will fromow on be referred to as ‘de-borated water’ and the tap waters ‘borated’ water. The local concentration of de-borated fluid

as measured above the core support plate (Fig. 3) by means ofgrid of conductivity probes.

The layout of the cold-leg pipes can be seen in the views ofhe CAD model in Fig. 4, and in a view from below in Fig. 5.

T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589 579

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pwttcts

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Fig. 6. Perspective view of vessel showing three of the four thermal shields andtflfi

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Fig. 4. Perspective view of the CFD model, and orientation convention.

n the global coordinate system indicated in these Figures, theertical coordinate, Z, was defined to be zero at the level ofhe centre of the main inlet pipe (the RCS pipe), and is directedpwards. Both X and Y coordinates are zero at the core axis, withaligned with the axis of the section of the RCS pipe joining

he downcomer. Positive angles are to the right of this positionnd negative angles to the left, viewed from above (Fig. 4). Theold legs carrying low flow out of the model are defined as theeft and right loops. Other model details are shown in Fig. 6.

The Reynolds number was one-tenth of that in the real powerlant; for example, 78000 in the downcomer at the transient timehen the de-borated slug reached the measuring plane below

he core inlet. The transient ramp length was adjusted so that

he Strouhal number (the ratio of forces due to transient andonvective accelerations) was the same in the test vessel as inhe plant. Dimensionless concentrations for mixtures of the twoolutions were obtained by means of 181 probes located 70 mm

ig. 5. View of CAD model from below, showing cut-away support plates, inletipes, and penetrations.

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he support blocks in the downcomer (light green), inlet pipes (light brown) anduid slug (dark brown). (For interpretation of the references to colour in thisgure legend, the reader is referred to the web version of the article.) .

elow the lower core plate, at Z = −1.129 m (Fig. 3). Verticalnd tangential/circumferential velocities in the downcomer wereeasured using Laser Doppler Velocimetry.

. CFD modelling

The CFX-5.6 version of the code was used for most steady-tate simulations, and the later version, CFX-5.7, was used forll transients. The advantage of the latter version lay solelyn its greater selection of turbulence models, and improve-

ents to some existing models. However, none of these changesnfluenced the conclusions drawn from calculations already per-ormed with CFX-5.6.

After a study of mesh effects made at Vattenfall, Grids 1nd 2 (the latter being a 1/2 × 1/2 × 1/2 subdivision of Grid 1)ere created using the FLUENT preprocessor Gambit, apply-

ng the ERCOFTAC ‘Best Practice Guidelines’ (Casey andintergerste, 2000). Hexahedral cells were used for the inlet

ipe, the downcomer and the upper 5/6th of the core, to obtainhe greatest accuracy of solution, while tetrahedral cells weresed, for convenience, in the lower plenum, the holes in the coreupport plate, the volume between the core support plate andhe core inlet plane, and the lower 1/6th of the core. A layer ofrisms was applied at the lower plenum wall, and pyramid cellss the transition between hexahedral and tetrahedral cells.

In addition to following the recommendations of the ERCOF-AC guidelines, consideration was also taken of work beingerformed in the parallel EU 5th Framework ProgrammeCORA project (Scheuerer et al., 2005), from which guidelinespecifically applicable for reactor safety analysis were derivedMenter et al., 2002). These covered the assessment of exper-ments for their suitability for code validation, the consistentnd correct use of CFD methods, and procedures for estimatingumerical and modelling errors in CFD simulations.

Four new grid models were created after FLOMIX-R had

nded (Grids A to D, with differences detailed in Table 1), tory to reduce the number of grid cells while not degrading theomputational accuracy of solution. The numbers and types ofells of all grids are summarised in Table 2. Some internal struc-

580 T.V. Dury et al. / Nuclear Engineering

Table 1Details of Grids A, B, C and D

Grid Thickness of both lower plenumsupporting plates (mm)

Centringblocks

Inlet pipe

A 17 Included Long, bentB 17 Not included Long, bentCD

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Simulations were made using the following turbulence mod-els: Standard k-�, RNG (Renormalised Group) k-�, Standard k-�and shear-stress transport (SST) k-� models, and a number of

TC

G

12ABCD

0 Included Long, bent17 Included Short, straight

ures were omitted in all grids, such as the vertical support rodsnd lowest supporting plate in the lower plenum, and small struc-ures and protrusions in the downcomer. Some internal structuresere simplified, e.g. not modelling the chamfers on the ther-al shields (Grids 1 and 2), or the lower plenum supporting

late thicknesses. Calculation with Grid 1 without any support-ng plates in the lower plenum had showed that their omissionignificantly de-stabilised the flow, and so they were retained forll simulations referred to here.

For all grids, the core was modelled as a porous volume withn inertial momentum sink. The resistance coefficients per unitength, based on the superficial velocity, were set to 2.28 m−1

or the vertical direction and 95.9 m−1 for the horizontal direc-ion, estimated from the VDI-Warmeatlas (VDI-Verlag, 1977),ith a volume porosity of 0.559. The core inlet and outlet platesad both been modelled with FLUENT as surfaces with inertialomentum sinks, with inertial resistance coefficient estimated

rom the handbook of Idelchik (1996) to be 12.3, based onhe superficial velocity. However, as CFX-5 could not represent

omentum sinks at surfaces, these surface sinks were combinedith, and distributed over, the sink over the full length of the

ore. After sensitivity studies with FLUENT, the CFD modelxit plane was set at the core outlet.

Steel walls were modelled with a roughness height of.15 mm (thus modifying the wall function), but the Plexiglas®

alls with zero roughness. The blocks centring the core barrelithin the vessel were included in all grids except B. Verticaloles in the core support plate were modelled explicitly.

In Grids 1 and 2, the two cut-away horizontal support platesn the lower plenum (Fig. 5) were modelled as simple two-imensional surfaces, i.e. with no vertical thickness, and located

ertically at the upper plate surfaces, but only minor simplifica-ions were made from the outlines of the actual manufacturedarts. However, the four grids A, B, C and D differed in theay that the support plates, centring blocks and inlet pipe were

Fo

able 2ells and their types for all grids

rid Number and type of cells

Inlet pipe Downcomer Lower Plenum (to cor

20224 (Ha) 106695 (H) 61781 (Ta + layer of P161792 (H) 853560 (H) 494248 (T + layer of P

63000 (H, incl. part of lower plenum) 324000 (T + 20000 Py63000 (H, incl. part of lower plenum) 324000 (T + 20000 Py63000 (H, incl. part of lower plenum) 324000 (T + 20000 Py58000 (H, incl. part of lower plenum) 324000 (T + 20000 Py

a H, hexagonal; T, tetrahedral; Pr, prism; Py, pyramid.

and Design 238 (2008) 577–589

reated, as described in Table 1. For Grids A to D, the inlet pipe,owncomer and part of the lower plenum were modelled withexahedral cells, the rest of the lower plenum was meshed withetrahedral cells, and the core meshed with prisms. Pyramidsonnected hexahedral and tetrahedral cells.

A simplification made for Grids A, C and D was that a slipoundary condition was set for the centring blocks, as theirimensions were smaller than those of the grids in this regionnd thus the code could not in any case resolve the velocityrofile over them.

During the transient, Fortran functions representing mea-ured inlet and loop outlet flow-rates were used instead of bynterpolation from the actual measured data. As all flow-ratesere zero up to 1.5 s, transient calculations were started at

= 1.5 s. Radial and tangential velocities were set to zero. Thenlet turbulence intensity and the hydraulic diameter were seto 10% and 5 mm, respectively. Putting the inlet boundary farpstream of the downcomer reduced the need for sensitivityests, and therefore no tests on its position or the boundaryonditions were made. The two loop outlets were positionedpproximately three diameters downstream of the downcomer,nd the flow-rate functions applied across the outlet planes. Noensitivity tests were made for the position and condition forhese outlets, as they were believed not to be important for theow field in the downcomer. The mass flow-rates applied by theunctions are plotted in Fig. 7 (note that the mass flow-rates inhe left and right loops are negative, i.e. the flows are out of the

ig. 7. Absolute mass flow-rates applied at the inlet pipe and the left and rightutlet loops.

e) Core Total

ra at wall) 12026 (H for upper 5/6 and T for lower 1/6) 200726r at wall) 96208 (H for upper 5/6 and T for lower 1/6) 1605808a) 27999 (Pr) 434000) 27999 (Pr) 434000) 27999 (Pr) 434000) 27999 (Pr) 429000

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T.V. Dury et al. / Nuclear Enginee

ifferent versions of the Reynolds stress model (RSM). The com-lete range of sensitivity tests was only made for steady-stateonditions and for the coarse grid. For transient calculations, theNG, SST and one of the RSM models in the code were used,ith both coarse and fine meshes.The default incomplete lower-upper (ILU) factorisation tech-

ique applied to the additive-correction algebraic multi-gridethod was used throughout, as was the improved Rhie–Chow

cheme for pressure/velocity coupling. The 1st-order upwindnd the high-resolution schemes for advection were applied andesults compared. The latter scheme blends 1st-order and 2nd-rder resolution according to the local gradient of the variableefined, and avoids numerical difficulties, which can occur withpurely 2nd-order scheme (see the CFX-5 code description

ANSYS, 2006) for details of the options).For the k and � terms in the appropriate turbulence equa-

ions, the 1st-order scheme was default and not intended to behanged, as it could be unstable. The high-resolution schemeas, however, applied for these terms for some calculations, butith no obvious benefit. During the fine-mesh transient calcula-

ion (Grid 2) with the RNG model, the high-resolution schemeaused numerical instability between 4 and 6 s and was replacedy the 1st-order upwind on all variables. The calculation subse-uently ran successfully from 6 to 25 s with the high-resolutioncheme. The high-resolution scheme caused no such instabilityith the other two turbulence models when used with Grid 2.A constant time-step of 0.01667 s was used for all transients,

orresponding to the sampling frequency of the experimentalata collection. This time-step gave a maximum Courant numberf around 30 with Grid 1. The only time-step sensitivity studyas made with Grid A (see below). The 2nd-order Backwarduler scheme was always used for time, with the solution forach time-step initialised from the end of the previous one.

Convergence was smoother and lower ultimate residuals werechieved with 1st-order upwind advection, due to the influ-nce of numerical diffusion, compared with the high-resolutioncheme, which tended to give stable velocities but fluctuatingMS residuals. To check if fluctuating residuals were caused by

nstability of the flow field, a transient calculation of steady-stateonditions was made with the RNG model and the coarse mesh.ith a time-step of 0.01 s (less than the default value of 0.042 s

et by the code), and for almost 700 time-steps, the calculated

mtl

Fig. 8. Vertical levels for ve

and Design 238 (2008) 577–589 581

elocities and residuals still fluctuated. A normalised RMS resid-al limit of 10−6 for iterations within each time-step was set foromentum, pressure and turbulence quantities for all transients,

s this was estimated from the steady-state calculations to be aufficiently low value to ensure adequate convergence. As thisimit could always be achieved with single-precision arithmetic,ouble-precision was never used (though it had to be used withLUENT to reach this convergence level with transients).

Initial boron concentrations were set in the volume contain-ng the slug of de-borated water (concentration = 0.0) and in theemainder of the facility (concentration = 1.0). The calculationas isothermal, with a water temperature of 53.6 ◦C, density of86.42 kg/m3 and dynamic viscosity of 5.156 × 10−4 N s/m2.

. Results

.1. Steady-state results: Grids 1 and 2

Comparisons were made for vertical velocity, tangentialelocity and velocity angle (flow direction) at two levels in theowncomer, one level at the middle height of the downcomernd one level closer to the bottom. Measurement positions arehown in Fig. 8.

Measured and calculated radially averaged vertical velocitiesre plotted in Fig. 9 for the lower vertical level in the downcomer.ualitative agreement is good, and important non-symmetry in

he flow field is visible. Below the inlet duct, however, the pro-ortional difference is large. This could be caused by the code’snability to model the wakes adequately behind the two hot-legucts passing through the downcomer close to the inlet ductpositioned at −50◦ and +70◦ azimuthally from it), as they fluc-uate in time, and it is impossible to represent this correctlyith a steady-state calculation. The difference could also beue to lack of resolution of the velocity field in the simulationf the stagnation zone resulting from the cold-leg jet impinge-ent on the inner downcomer wall, which was not investigated

or mesh sensitivity effects and is a difficult region to correctlyodel.

Table 3 lists quantified differences between calculations and

easurements for steady-state velocities, showing that devia-ions are higher at the middle level in the downcomer than at theower level.

locity measurements.

582 T.V. Dury et al. / Nuclear Engineering

Fig. 9. Radially averaged vertical velocity at the lower level in the downcomeras a function of tangential angle (Grid 2).

Table 3Quantified differences between CFD calculated and measured velocities in thedowncomer

Vertical position Velocity component DEV3 ABS

Middle level in downcomer Vertical 0.39Middle level in downcomer Tangential 0.59Middle level in downcomer Velocity angle 29◦Lower level in downcomer Vertical 0.21Lower level in downcomer Tangential 0.32Lower level in downcomer Velocity angle 13◦

D

waiim

D

a

D

wv

Zfta

t

Fig. 10. Vertical velocity component at plane Z = −1

and Design 238 (2008) 577–589

The absolute deviation DEV3 ABS, is defined as:

EV3 ABS = 1

n

n∑

i=1

DEV2i ABS (1)

here n is the number of measurement positions used for aver-ging, i.e. the total number of measurement positions in the corenlet plane, and DEV2 is an accumulated deviation at positionover the important time span, i.e. when the perturbation isoving through the measurement plane:

EV2i ABS =t=t2∑

t=t1

|DEV1i|t (2)

nd

EV1i,t = cc,i,t − cm,i,t (3)

here cc is the calculated, and cm the measured, value of theelocity at position i and time t.

Vertical velocity component at the vertical elevation= −1.129 m, below the core, is plotted in Fig. 10(a–d), viewed

rom above, for different turbulence models but always with

he high-resolution discretisation scheme (the velocity field waslways more diffuse with upwind discretisation).

The RSM model produced a slightly greater azimuthal rota-ion of the velocity field than the RNG model, but with reduced

.129 m; different grids and turbulence models.

ring and Design 238 (2008) 577–589 583

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Fig. 12. y+ Contours: Grid 2.

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T.V. Dury et al. / Nuclear Enginee

esolution (NB. all plots have been produced with the sameelocity scale range, for clarity of comparison). Velocity dis-ribution with the RNG model and the fine grid, Grid 2, isiven in Fig. 10(d), showing that the resolution of the veloc-ty field is significantly improved with this mesh. Discrete fluidets emerging from the holes in the core support plate are visi-le, and the region of upward velocity in the downcomer belowhe inlet duct (showing the presence of strong recirculation)hows clearer and stronger resolution across the downcomerhickness.

The conclusion was that the RNG model with high-resolutioniscretisation gave best agreement with measurements forteady-state conditions with the coarse mesh model, and con-equently it alone was used for the fine-mesh steady-stateimulation. This had also been the conclusion from earlier FLU-NT calculations at Vattenfall. Scalable wall functions were thenly choice with this model.

.2. y+ Values: Grids 1 and 2

Examination on the inner downcomer wall, the hot and coldoop pipe wall, and on the inside of the lower plenum showshat the peak value of the dimensionless wall–cell distance,+, for the coarse mesh steady-state simulation with RNG tur-ulence model and high-resolution advection scheme reachedver 19000. This maximum occurred at the hot-leg penetrations,hich is not expected to produce a significant error in the cal-

ulation of the flow field in the vessel as a whole. Contours of+ are plotted over these surfaces in Fig. 11, with a peak plot-ing scale range of 0–4500 (4500 is close to the value in thempact region of the incoming cold-leg flow on the downcomerall).Even with Grid 2, the peak y+ value reached over 12000 at

he hot-leg outlets. However, the values within the body of the

essel are plotted over the range 0–2400, giving the pattern seenn Fig. 12, with the value at the impact region of the incomingold-leg flow close to 2400. On the basis of these y+ values,he turbulent wall functions are being used well outside their

Fig. 11. y+ Contours: Grid 1.

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Fp

ig. 13. Mean dimensionless boron concentration at core inlet as a function ofime.

ange of applicability for the k-� model (validity 30 < y+ < 120n CFX-5) throughout most of the vessel, even with the fine-grid.hus, the mesh must be further refined for the wall functions to

e validly applicable everywhere, and no results obtained herean be considered to be mesh-independent.

ig. 14. Minimum relative boron concentration at core inlet (independent ofosition) as a function of time.

584 T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589

boron concentration: Measurement left; CFD right.

4

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tFigs. 16–19 show measured and calculated radially averagedvertical velocities as a function of time at the middle and lowermeasurement levels in the downcomer, respectively. The mea-

Fig. 15. Time-independent minimum relative

.3. Slug-mixing transient: Grids 1 and 2

Mean and minimum dimensionless boron concentration athe core inlet as a function of time, with Grid 2, the RNG modelnd high-resolution discretisation, are shown in Figs. 13 and 14.he CFD calculation gives approximately the same minimumalue, around 0.8, as the experiments. The calculated mean andinimum concentrations are, however, delayed by around 0.9 s

ompared to the measured values. This is thought to be dueo inaccuracy in the measurement of flow-rate. The mass flowignal was filtered in time in the flow meter, at a level, whichould not be reduced further. This resulted in a time delay in theutput signal of about 0.7 s for the first indication of the slugeaching the core inlet, compared with the CFD calculations.

Fig. 15 shows measured and calculated minimum boron con-entrations, independent of time, at the core inlet. The inlet pipes positioned to the right and the view is from above. It can beeen that the calculated minimum is separated from the mea-ured minimum by about 180 mm, at the model scale of 1:5 (orround 0.52 R, where R is the radius of the core inlet plane).he displacement of the concentration field is, however, mainlyzimuthal. The difference in radial position is only about 0.15. This could be relevant in reality, as a core is primarily dif-

erent radially, as far as fuel enrichment and core reactivity areoncerned.

Two “islands” of low boron concentration are present in theeasurement and the CFD calculation, and the calculated min-

mum concentration field shows more variations in space thanhat measured. The plot from the measurement is based on dataor the average of five tests. Also, it should be pointed out thathis is a result from a calculation that has not been verified to berid or time-step independent.

The absolute deviation from experimental values of dimen-ionless boron concentration (DEV3 ABS) is 0.1228. A timehift of 0.9 s of the calculated values has been applied as well asspace shift of 176 mm, corresponding to the deviation in calcu-

ated position of the minimum concentration. Comparisons arenly made over the time span when the lowest concentrationsre measured, from 11.0 to 12.0 s. Comparisons are only maderound the position where the minimum concentrations were

Fd

ig. 16. Measured radially averaged vertical velocity at the middle level in theowncomer.

easured, over an area of 0.00915 m2 (i.e. 2.8% of the wholeore inlet). This area encompasses the area for seven probe posi-ions, corresponding to a radius of 54 mm. Only six of the sevenrobes were used in the comparison, as one of them was out ofrder during the measurements.

One reason for calculating incorrect boron concentrations athe core inlet can be that the calculated velocity field is wrong.

ig. 17. Calculated radially averaged vertical velocity at the middle level in theowncomer.

T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589 585

Fd

sat

iltqefi

Fd

bivpi

ig. 18. Measured radially averaged vertical velocity at the lower level in theowncomer.

ured velocities shown here are averaged over a time span ofbout 1 s. Most of the fluctuations in the measured signals areherefore not visible.

It can be seen from these figures that the rather abrupt changen flow direction at around 7–10 s in the measurement at theower level in the downcomer, and the following transition

o a fully turbulent steady-state flow pattern, are not captureduite accurately by the CFD calculation. This will have anffect on the mixing and transport of the boron concentrationeld.

c

bp

Fig. 20. Horizontal velocity component at vertical

ig. 19. Calculated radially averaged vertical velocity at the lower level in theowncomer.

Flow distribution within the vessel is strongly influencedy the velocity profile at the exit of the inlet pipe. If this isncorrectly calculated, its effect will continue throughout theessel. Shaded contours of horizontal velocity at the verticallane where the inlet pipe joins the downcomer are plottedn Fig. 20(a–d), showing differences resulting from CFD grid

oarseness and turbulence model.

The view in these figures is in the direction of flow, so theend, which is about 3 hydraulic diameters upstream of thisoint, has caused the region of very low fluid velocity on the

inlet plane of cold leg to downcomer at 10 s.

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86 T.V. Dury et al. / Nuclear Enginee

eft-hand side of the inlet plane, with the RNG model and Grid. There is little visible difference between the profiles withhe SST and RSM models, and only a small distortion of theelocity profile on the left-hand side. Isosurfaces at the frontnd back ends of the de-borated slug (not reproduced here) alsoonfirmed that the RNG velocity profile is more strongly peakednd distorted than with the other turbulence models.

. Further grid studies: modelling

The high-resolution discretisation scheme was used for allalculations with Grids A to D, using the standard k-� and RNG-� turbulence models. A normalised RMS residual criterion of

0−5 was set for steady-state convergence, while this was relaxedo 10−4 for transients (the default value in all versions of CFX-5,nd still recommended in CFX-10). Time-step sensitivity wasxamined with Grid A, using steps of 0.01 s and 0.017 s.

toii

Fig. 21. Effects of the centring blocks and

and Design 238 (2008) 577–589

. Further grid studies: steady-state

The effects of the centring blocks and shape of the inletipe can be seen in Fig. 21(a–e). From Fig. 21(c) (Grid A) andig. 21(e) (Grid D), it can be observed that the swirl of theow generated by the bend in the inlet pipe changes the shapend location of the vortex in the vessel. Indeed, in the solutionbtained with Grid A, the region of the upward vertical velocityn the downcomer is displaced in the counter-clockwise direc-ion compared with the solution obtained with Grid D. However,he swirl seems to have no noticeable effect on the flow at theore inlet. On the other hand, comparing Fig. 21(a) and (b), andig. 21(c) and (d), it can be seen that the result of introducing

he centring blocks into the model of the vessel is similar to that

f changing the shape of the inlet pipe: the position of the vortexn the downcomer is altered, but the flow distribution at the corenlet stays practically unaffected.

shape of the inlet pipe on the flow.

T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589 587

comer

atibwstvtsl

7

vwCtA

Fu

Fig. 22. Radially averaged steady-state vertical velocity in the down

These results imply that, despite the fact that the flow velocityt the core inlet is not affected by the shape of the inlet pipe andhe presence of the centring blocks, these objects change the flown the downcomer significantly, and this suggests that they muste included in the model of the vessel for transient simulations,here the distribution of the flow velocity in the downcomer

trongly affects the transport of the slug of de-borated waterhroughout the complete vessel. Comparing radially averaged

ertical downcomer velocity with Grid A in Figs. 22 and 23,he k-� model results are closer to the data at the lower mea-urement level, while the RNG model is closer at the middleevel.

es

m

ig. 23. Boron concentration at core inlet, RNG: (a) mean and (b) minimum. Line apwind.

Fig. 24. Boron concentration at core inlet, RNG: (a) mean and (b) minimum

: lower level (a) Z = −1.0033 m and (b) middle level, Z = −0.773 m.

. Further grid studies: transient

On the basis of comparison of the resolution of steady-stateelocity field presented in Fig. 21(a) and (c), the RNG modelas chosen for the transient simulations, with Grids A, B andonly. There was no significant difference between predicted

ransient results using time-steps of 0.01 s and 0.017 s, with Gridand both turbulence models, so the larger value (i.e. the actual

xperimental data acquisition rate) was chosen for all followingimulations, to minimize computational time.

The closest agreement with experiment for mean and mini-um boron distribution at the core inlet was obtained with the

= Grid A, high resolution; Line b = Grid B; high resolution, Line c = Grid A,

. Line a = Grid A, high resolution; Line b = Grid C, high resolution.

588 T.V. Dury et al. / Nuclear Engineering and Design 238 (2008) 577–589

Rio(tcs

iFwamimb

atcifge

8

(

Fig. 25. Boron concentration at core inlet plane: Grid A, RNG.

NG model, high-resolution discretisation and Grid A, as shownn Figs. 24 and 25. It can be seen in Figs. 23 and 24 that modellingf the thickness of the supporting plates in the lower plenumGrid A) gives slightly closer agreement of mean boron concen-ration at core inlet than with zero thickness and only form-lossoefficients. For minimum concentration, the difference is evenmaller.

For the overall distribution of boron concentration at the corenlet at the time when the minimum occurs, it can be seen inig. 25 that the RNG model with Grid A agrees more closelyith measurement (Fig. 26) than Grid 2 does (Fig. 27), as far

s degree of rotation about the vessel axis is concerned. Theagnitude of the minimum is very similar in all three plots, and

n the same quadrant. However, the physical separation of the

inima in the two “islands” of low concentration is smaller for

oth CFD simulations than was measured.

Fig. 26. Boron concentration at core inlet plane: experiment.

(

(

(

Fig. 27. Boron concentration at core inlet plane: Grid 2, RNG.

With Grid A, the weaker region of low concentration reacheslower level than measured and is of greater extent, thus showing

hat the splitting and mixing of incoming flow is still not quiteorrect. Nevertheless, results with this grid demonstrated that its possible to obtain very close overall and absolute agreementor minimum concentration value at the core inlet plane with arid, which is only a quarter of the size of Grid 2, the finest usedarlier.

. Conclusions

1) CFD calculations have been carried out on the experimentVATT-02, in the context of the FLOMIX-R EU 5th Frame-work Programme, to assess the capability of the CFX-5 andFLUENT codes in simulating boron dilution transients in aPWR Reactor Pressure Vessel.

2) Steady-state isothermal simulation was made initially withtwo grids, an initial coarse mesh and one refined by a factorof 2 in all three dimensions. The RNG turbulence modelgave results which were the nearest to measured velocitiesin the downcomer, with both meshes and for both codes.The reason why the RNG model is better than more sophis-ticated models, which can better resolve complex featuresof flows, is most likely because none of the models is beingused with the correct range of wall–cell thickness, and thefeature of the RNG model to compute lower production ofturbulent kinetic energy for flow over obstacles may dealmore accurately with the situation with this vessel geometry.

3) CFX-5 results were closer to measurement, with both grids,than those obtained at the initial analysis stage with FLU-ENT.

4) For a pump start-up transient in which a slug of de-borated

water in the only operating cold leg was injected at anincreasing rate, the SST model gave a minimum boronconcentration over the core inlet which was about 25%above that measured. The RSM model was 25% lower

ring

(

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A

C

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T.V. Dury et al. / Nuclear Enginee

than the data, while the RNG model and the fine meshgave closest agreement with the minimum measured. How-ever, mesh-independence of any of the results was notproven.

5) With a new set of grids, having 27% of the number of cellsin the fine-mesh model previously used, it was shown that:(a) it is essential to model any bends in the inlet ducting;(b) mixing is improved if the thickness of the supportingplates in the lower plenum is modelled; (c) rotation of flowaround the vessel axis is in better agreement with experimentwhen the thermal shields in the downcomer are not included,suggesting that modelling of structures in the downcomer isstill not correct.

6) Further simulation is needed to demonstrate the importanceof including the thermal shields, their chamfered edges, andthe support columns in the lower plenum. Also, the workshould be continued, as more powerful computer systemsbecome available, to refine the mesh further until mesh-independent results have been obtained.

7) Overall, it can be concluded that the present CFD study hasshown closer agreement of boron concentration prediction

at the core inlet than had been achieved in earlier work, withother experiments. However, care is needed in the modellingof individual components of a reactor vessel and its asso-ciated ducting in order to accurately capture the features

T

V

and Design 238 (2008) 577–589 589

which influence the mixing and control the flow directions,for the particular turbulence model used.

eferences

NSYS Inc., 2006. CFX–5 code description (recently re-named ANSYSCFX–10), Canonsburg, Pennsylvania, USA, http://www.ansys.com/.

asey M., Wintergerste T., 2000. Best Practice Guidelines. ERCOFTAC SpecialInterest Group on Quality and Trust in Industrial CFD.

LUENT Inc., 2005. http://www.fluent.com/.delchik, I.E., 1996. Handbook of Hydraulic Resistance, third ed. Begell House

Inc, ISBN 1-56700-074-6.enter F. et al., 2002. CFD best practice guidelines for CFD code validation for

reactor safety applications. ECORA EU project. EVOL-ECORA-D01.ohde U., Kliem S., Hohne T., Hemstrom B., Toppila T., Elter J., Bezrukov Yu.,

2005. The EC Project FLOMIX-R – Investigation of Fluid Mixing and FlowDistribution in the Reactor Circuit. Annual Meeting on Nuclear Technology2005, Session: Application of CFD Methods in Nuclear Reactor Safety,Nuremberg, Germany.

ohde U., Kliem S., Hemstrom B., Toppila T. and Bezrukov Y., 2005. Descrip-tion of the slug mixing and buoyancy related experiments at the different testfacilities (Final report on WP 2). EU 5th Framework Programme 1998-2002,FLOMIX-R Deliverable D09, FIKS-CT-2001-00197.

cheuerer, M., et al., 2005. Evaluation of computational fluid dynamics methods

for reactor safety analysis (ECORA). Nucl. Eng. Des. 235, 359–368.

uomisto H., 1999. Final report: EUBORA concerted action on boron dilutionexperiments. EU 4th framework programme on nuclear fission safety, AMM-EUBORA (99)-P002.

DI-Verlag GmbH., 1977. VDI-Warmeatlas. Dusseldorf.